The Dynamics of Coupled Planar Rigid Bodies.
Part II: Bifurcations, Periodic Solutions, and Chaos

Oh, Y. G., N. Sreenath, P. S. Krishnaprasad, and J. E. Marsden

J. of Dyn. and Diff. Eq., 1 (1989), No. 3, 269-298

Abstract:

We give a complete bifurcation and stability analysis for the relative equilibria of the dynamics of three coupled planar rigid bodies. We also use the equivariant Weinstein-Moser theorem to show the existence of two periodic orbits distinguished by symmetry type near the stable equilibrium. Finally we prove that the dynamics is chaotic in the sense of Poincare-Birkhoff-Smale horseshoes using the version of Melnikov's method suitable for systems with symmetry due to Holmes and Marsden.